Diaphragm mounting



Feb. 13; 1951 Fild June 15, 1946 F. SLAYMAKER ETAL DIAPHRAGM MOUNTING 10A. F. MIXER H. F. 81g AMPLIFIER STAGE AMPLIFIER 5 SAW #TOOTH BAND PASSOUTPUT OSCILLATOR FILTER STAG E LY N BY FRA INVENTORS WILLARD F. MEEKERN L. MERRILL NK a. SLAYMAKER ATTORNEY 2 Sheets-Sheet 2 INVHVTORS WILLARDF. MEEKER LYNN L. MERRILL FRANK H. SLAYMAKER ATTORNEY OBY . H. SLAYMAKERL- DIAPHRAGM MOUNTING O n Om nd nm Od- Om- QT 07 Q7 9 DAY n I Feb.'13,1951 Filed June 15, 1946 Patented Feb. 13, 1951 Y uN T o STATES PATENTomcc DIAPHRAGM MOUNTING Frank H. Slaymaker, Willard F. Meeker, and LynnL. Merrill, Rochester, N. Y., assignors to Stromberg-Carlson Company, acorporation of- New York V Application June 13, 1946, Serial No. 676,425

' 11Claims. (Cl.18131) This invention relates to transducers and more 7particularly totransducers having directional characteristics.

In manysituations in which it is not possible patterns of a typicaldisk-like vibrator under dif- 1 ferent conditions, Fig. 4 is a set ofcurves helpful inunderstanding and practicing the principles of thisinvention, Fig. 5 isa graph showing the presto determine the location ofan object visually, 5 sure distribution which corresponds to the beam itis desirable to provide signals which will serve of radiation of atypical application of this into locate such objects. For example, itmay be vention, Fig. 6 is a representation of a carbon desirable toprovide an audible signal which granule or sand pattern showing the modeof varies in a characteristic such as pitch, whenvibration of the diskused to obtain the direccver the observer, such as a blind personcarrytional or pressure characteristics of Fig. 5, Fig. ingtheapparatus, approaches an object or when- 7 is a graph showing thedirectional pattern or everan object moves with respect to the observer,pressure distribution of a diaphragm operating asthe case maybe. l at anon-normal mode, Fig. 8 is a sand pat- In, a co-pendin ited-st tapplication.gf tern of a non-normal single circular mode of Willard F.Meeker and Frank H. Slaymaker, 'sevibration corresponding t tdistribution p trial No. 607,840, filed July 30, 1945, now attern ofFig. '7, Fig. 9 is a calculated pressure disent No. --2,474,918, issuedJuly '5, 1949,. d tribution' graph of one embodiment of our invensignedto the same ass gnee as t present, tion, Fig. 10 is a measured pressuredistribution ventiomthere is described and claimed a pulsed graph usingthe sk o which the graph of frequency modulation system for ascertainingFig. 9 was calcul and F ll is a sand or the location of unseen objects.In this system, carbon r n pattern tr tin the m d of there is em loyed asingle in t for generatvibration of the transducer disk utilized inconing continuous oscillations varying cyclically. as nection with Fi s.9 and to frequency within a given-band of frequencies. Referring to Fig.1 of the drawings, there'is Oscillations within only a part of this bandare illustrated in block form the system described radiated periodicallyand echos reflected from and claimed indetail in the aforementionedapvarious objects are received and combined with plication. There isprovided asuitable oscillathe continuous oscillations to produce a beatt L'Wh ay be o the resistance-Capacitance note which varies in characterwith the d stance or phase-shift type, for example. The frequency to theobject. The beat note is translated into of oscillation may be varied insuitable manner sound, the pitch varying with the distance'to the as bymeans of'a sawtooth oscillator 2. s In order object. r p to, limit theextent of the radiated frequencies,

It is an object of this invention to provide a there is provided asuitable band-pass filter 3. transducer suitable for use in a locatingor rang- The fi d output is passed through an Output ing system such asthat briefly described above, st e 4 to a d rect o r to 5 from which forexample, and which has a desired directional radiations are emitted.Reflections or echoes characteristic. from objects against which theradiation im-..

Incarrying outthe objects of the invention; pinges are picked up by areceiver or microth'ere is employed a reflector having a suitable phone6 which may be identical to the radiator disk-like diaphragm and-thediaphragm is so 40 5, amplified by a'suitable high frequency amplidimensoned and is driven in such a manner that fier l and combined in themixer sta 8 w substantially --all of the radiation from thediaoscillations derived from oscillator l to develop phragm is directedtoward the side walls of the a beat note which may be amplified in anaudio reflector, and symmetrically with respect to the frequencyamplifier 9 and translated into sound axis of the reflector. As aresult, a sufiicientlysignals in sound reproducing means, such asdirective beam of radiation is obtained. headphones l0.

Other objects and advantages of this inven- The radiator unit, as wellas the microphon or tion will be understood from a reading of thereceiver unit, are preferably of a resonant magfollowing specificationin conjunction with the netostrictivetype. Referring to Fig. 2, a transcpany ng drawings in which Fig. 1 is a block .50 ducer embodying theprinciples of our invention diagram illustrating a suitable form ofranging comprises a driving unit made up of a suitable ol -locatingsystem, Fig. -2 is a sectional view of a polarizing magnet ll mountedbetween a gentransducer built in accordance with the prinerallyU-shaped. 'polepiece l2 and an apertured ciples of this invention; Fig.3 is a series of polar polepieoe l3. A hollow cylindrical tube l4, madegraphs showing calculated pressure distribution irom'a material havingmagnetostrictive characteristics, such as nickel, is fixed againstmotion at one end thereof as by means of a suitable plug l5 secured inone end of the tube M, a mounting plate i6 secured to the plug 15 bymeans of a suitable threaded fastening member I! and additional threadedmembers 18 extending through suitable openings in the member 16 intothreaded engagement with the adiacent portion of the polepiece I2.Suitable spacers 24 may be employed if necessary. The free end of thetube I l extends axially through the openin in the polepiece l3 and hasa disk-like diaphragm [9 secured thereto as by means of solder. Thetransducer unit also comprises suitable means for causing pressure wavesresulting from the vibration of the diaphragm I9 to be directed outotherthan resonant frequencies, radial or diawardly in a beam of desiredconfiguration. We

prefer a parabolic horn or reflector of suitable material, such as woodor spun aluminum, for example. The reflector has an opening 2! in itsrestricted end to receive the diaphragm or disk. The driver'unit and thereflector may be joined together in any suitable manner (not shown).Preferably, the horn and driver unit are separated by suitable vibrationinsulating material in Order to prevent mechanical couplin between thehorn or reflector and the driver unit. The length of the tube It and theconstruction of'the reflector are such that the diaphragm I9 is locatedapproximately in the plane of the latus rectum of the reflector 20normal to the axis thereof. The signals appearing in the output of theoutput stage 4 are impressed across a suitable driving coil 22 which inthe illustrated form of this invention encircles the tube M. Anysuitable mounting means may be provided for the coil 22. The permanentmagnets H serve as polarizing magnets and maintain a magnetic fieldthrough the tube l4. Whenever the flow of current through coil 22 variesin accordance with the frequency changes of the oscillator l, themagnetic field at the tube is varied and because of the magnetostrictiveproperties of the tube 14, the length thereof changes. Inasmuch as theleft hand end of the tube (as viewed in Fig. 2) is relatively fixedagainst movement, any resulting movement takes place at the diaphragmend of the tube. As a result of the foregoing, vibrations are set up inthe diaphragm l9 and pressure waves are emitted therefrom.

In order to enable the operator of the device to distinguish amongobjects, it is preferable to limit the reflections or response to arelatively few objects and hence it is desired to provide a radiatorwhich will emit radiation in a relatively sharp or small cross-sect onbeam of radiation. The choice of dimensions of the diaphragm areimportant in achieving the desired beam. Diaphragms of the typeillustrated in the drawings are caused to vibrate in modes which'can bereadily' observed by operating the unit with the diaphragm [9 in thehorizontal position and with the monies in the Fourier series. As thedriving frequency applied to the ob ect such as diaphragm I9 is varied,different conditions of resonance result- If-the diaphragm or. object isdriven at a I tion pattern.

metrical or more complex modes result.

There follows a mathematical analysis of the problems involved inproperly constructing and driving or exciting the diaphragm l9 andassociated parts in order to obtain the desired radia- This analysis isbased on a transducer as described above except that the diaphragm islocated in the plane of a, substantially infinite bafile instead of inthe plane of the latus rectum of the reflector. A high degree ofcorreelation has been found between results predicted as a result ofthis mathematical analysis and ex-fperimental results obtained. when thereflector used;

In-this analysis the following assumptions will be made:

(a) That the diaphragm Hi can be treated as a" free edge disk, (b)

diaphragm, 0)

tube M, (d)

under vibration) (e) That the amplitude of motion is small, and (j) Thatdamping, due either to friction or to.

acoustical radiation, can be neglected.

The C. G. S. system is used except where otherwise noted.

The following symbols will-be used:

Ro=distance from the centercf the disk to point P, =-angle between anormal line R0, W=deflection normal to the plane of the disk, z=mass perunit area of the disk, F(r) =F0(1') sin wt,

Fo(r)=maximum applied force per unit area of,

the disk,

E=Youngs modulus for elasticity for the disk material (10 for brass). ffor the disk material for-j v=Poissons ratio brass) That even thoughother modes of vibration, can exist only circular modes needbeconsidered, a circular mode of vibration being any mode of vibrationwhose amplitude'and phase are independent of angle around the That thedriving force on the disk l9 can. be f considered as concentrated at acircle con-"i centric with the circumference of the disk j and havingthe same diameter as the driving That the joint between the nickel tubeand the disk does not appreciably alter the (1y,- namic curve of thedisk (the dynamic curve corresponding to the cross-sectional shape of Ithe diaphragm at its maximum deformation' point on to the disk ndthflh=disk thickness in em., h"=disk thickness in inches,

Vo=normal velocity po=density of air, =density of the disk material (8.4for brass) p=pressure,

j=frequency of vibration, 1 c=velocity of sound in air (34,4() 3cm./sec.) (0:21), i

The differential equation of the vibrating disk 19, with slight changesin notation, has been shown to be (see Electromechanical Transducers andWave Filters by W. P. Mason, D. Van Nostrand Co., New York, N. Y., 1942,page 168, and an article by A. G. Warren, Philosophical Magazine, vol.9, page 881, 1930). IZ 2 6 W 1 6 W 55W n 5 W' F(r) 6r 1' 513 7* 512 1 6rD W T D The solution of (1) for the free vibrations of a free-edge diskmay be found by assuming the driving force F(r)=0 and using the methodof separation of variables. Thus, let

' Let each member of (3) be set equal to 0 (treated as a constant) andsolve. Then, using the usual notation for Bessel functions,

The boundary conditionsto be satisfied are:

(a) The displacement is nowhere infinite, (b) The shear is nowhereinfinite (c) The shear at r=a is zero, 7

(d) The radial stress at.r=a is zero.

The shearing stress per unit of are at any In order that the radialstress at r=a shall be zero it is necessary that r I Taking v= and makeuse of (8), 4: n( 50) (10) smf'Jmu) 1 u) Solving Eq. 10 by methods ofapproximation gives the values of X, for one, two, and three nodalcircles, as

respectively."

6 Then, from (7), (8) and (4), R takes the form where A may take: ononly the values given by Replace C3C5 by C1,. and CaCe by C'n. Let thesuccessive values of A be A1, A2, A3 An, and let fa fglaonr Home 13)Then, taking the solution of (1) as a summation of terms of the form RT,it follows that Eq; 14 is the general expression for the free vibrationsof the disk [9.

initial conditions the values of C11. and C'n may be found by familiarmethods.

For the forced vibrations assume a harmonic driving force of the form Fm=F0(T) sin it (15) Substitute.( 15) in (1) and observelthat theresulting equation may be satisfied by a solution of the form W =f(r)sin wt (16) where fCr) represents the dynamic deformation curve of thedisk l9. Sincelosses are considered negligible, there is no component ofthe velocity in phase with the drivingforce, and the displacement andthe driving force may be considered in phase. Substitutin (15) and (16)in (1) and removing the time factor, 7

Jlonwrlonw if (18) 1 Equations 18 make it possible to expand F00) andf0) in terms of @Outr). Thus take Substitute 19) and (2 0) in (17) andmake use of the fact that the left hand member of (17), except for thelast term, may be replaced by terms of the form m w Then, collectingterms With a given set of 7 Equating coefiicients of like terms bl 01/ Db2: a /D (22) b a /D n 4 l a R" De:

Now let F00) be zero for all values of 1- except r=ro, where To is theradius of the driving circle, and at m let F00) be such that L ney-era(2 Then multiplying (19) by rdr and integrating between the limits 0 anda it follows that Similarly multiplying by @0111) rdr, integrating andobserving that L F (1) I ()\,,r)rdr= I r it follows that a OnJo) V 4 Jo(v( n [ma fimaflrna) Making use of (22), Equation 20 for the dynamiccurve becomes f 0+2M.w.r)] (26) 11:1 where M n; and

M 1 IL O) D 4 0( n 0( n 2 [9 \?,a J ()\,.a)I \,,a) D

Inspection of (26) and (28) shows that at a resonant frequency where thecorresponding term in the expansion becomes infinite (since dampingefiects are neglected). In such case, except for a constant multiplier,the dynamic curve may be taken as f0) :QOVLT) At non-resonantfrequencies several terms in the expansion may be necessary. Such termswill .consist usually of the Mod. term and the Mn terms for which 2 D)is small. As will be shown later in determining the directionalcharacteristics the Mo/a? term is the only term which can producepressure at points on the axis of the diaphragm or disk I9.

The resonant frequencies of a given diaphragm or disk may be determinedfrom (29) Thus taking w=21rf The value of n gives the number of circlesin the normal mode Since Eh D 12 1 ---v and m=ph (31) may be writtenshowing that the frequency, for resonance in a specified mode isdirectly proportional to the diaphragm disk thickness h. For brass disksused in a physical embodiment of this invention, E was taken as (10), pas 8.4 and 1/ as Equation 32 then gives Taking An as 4.89 for the secondresonant fre quency, (from (11) and a =1.2'7 cm), and expressing h ininches, the

expression for 1 becomes Substituting Equation 11 and rearranging,Equation 32 may be written as I 21rf 5 E a 'v 12,1(1-11 where an is aconstant determined by the desired normal circular mode.

In order to analyze the directional characteristics, let it be assumedthat a free-edge disk hav- Let dA be a differential area in a vibratingdisk with polar coordinates (r, 0) relative to the center of the disk.Taking (26) as the equation of the dynamic curve of the disk, insertinga time factor e taking the derivative with respect to time, and thenremoving the time factor, it follows that In (34) R1 in the denominatormay be approxie mated as R0, and R1 in the exponent may be approximatedas (Ro-r sin 0 cos 0). Then, ex-' cept for a constant multiplier =LLZ1rf( ikr aindcos' or, upon evaluatingv the first integration 1J=21rJ;f(1") J 0 sin )rdr 37);,

Equations 13 and 26 show that for any fixed value of w,](1) is made upof terms of three types;

a constant term, a term of the form Jo Omnand, a

tltei'm of the form InOmT), Equation 3'7 may be evaluated for each ofthese three types and the results, with the proper multipliers, combinedfor .the complete expression for p. Thus a J Uca sin 4 ka sin 1) (38)JIJ Ucr sin I )rdr= ghocwmmr sin 4i)rdr= The complete expression forpressure, with the Zexception of a constant multiplier, then be- .comesEquations 2'7 and 28 may be used to find 11*0 pressure along'the axis.As the frequency deviates from resonance the term MoG plays a moreprominent role and the axial lobe increases in magnitude until, in somecases, it is much longer than the side lobes.. As the next resonant frequency is approached the axial lobe decreases j and reaches aminimum atresonance. Figure 3 1 size of the center lobe is a very criticalfunction or" the frequency, although good results are ob tained when thediaphragm is excited only ap- 1 proximately at the determined frequency.

Uncontrolled experimental factors, such as damping, which have not beenconsidered in the analysis could cause the experimental curve to differconsiderably from the calculated curve.

Variations in the assumed values of Youngs modulus and the density wouldshift the resonan frequency.

The entire analysis has, also, been based on the assumption that onlycircular modes of vibration exist. The desirability of having a mode ofvibration which is symmetrical about the axis gives some justificationfor the assumption, but it does ".ithe values of Mo and Mn for a disk ofa given material and dimensions, driven at a specified -fgreqriehcy,provided, of course, that the value of fin (9) may still be taken as /3.The dynamic curve may be obtained from (26) and the direc- "tiOIla1--characteristic from (41). At or near a resonant frequency thecorresponding value of -Mn, say Mn, will be very large relative to theother values sothat the dynamic curve may be considered as given by@Om'T) and the directional characteristic by (Pn+Qn'). Ins'pection ofEquations 43 and 44 shows that *when =0, -(Pn+2n) =0, so that, referringto -Equation41, the only term contributing to press'ure on the axis'isthe MoG term. At resonance this term is very' small relative to the term--Mn (Pn+Qn), and the pressure distribution con- --sists of side lobeswith a relatively smallaxial *i 'lobe. It'hasalready been shown that adisk will -vibrate' at resonance with two. nodal circles if n thefrequency is determined by (33). From the ,-:'.1 above it is apparentthat at resonance the radiaon is predominantly lateral. 'Neglectingdamping, the axial pressure is zero t resonance but the presence ofdamping, by reducing the amplitude of the resona'ntma'de ----relativetothe 'MoG term, always provides some not preclude the existence of radialmodes. Near a circular normal mode, however, there should be littletendency for radial modes to appear except in the unusual circumstancesin which a radial mode of vibration and a circular mode have the samefrequency. If some of the noncircular modes do appear at frequenciesbeing considered, the anlysis does not apply.

Table I of @(Mr) as a function of r, and Table II of G and (Pn-f-Qn) asfunctions of (10a sin have been prepared for disks of 1.27 cm. (0.50in.) radius made of any material for which 1/ may be taken as and arereproduced in this specification. They cover only the cases-of one, two,and three nodal circles but may be extended furtherflby use of Formulas13, 42, 43 and 44. In

using the tables it is necessary to know the disk 'thicknessh' and thedriving frequency f. The

computed values of M0 and Mn and the tablulated 'values of i \m) maythen be used in (26) to determine points on the dynamic curve. The samevalues of Mo and M1; and the tabulated values of G and (Pn+Qn) may beused in (41) to determine the directional characteristic.

In using Table IIit is necessary to determine finding is from theequation k=21rf/c=1 .825j (l0)-- (45) Table I.-.-Values of @(Mr) I [Tobe used in E q. 27 to determine dynamic curves] r/u (A11) (Mr) (M1)Table II values of G and (Pn+Qn) {To be used in Eq. 42 to determinedirectional characteristics] 1m 5111 45 G 1 Pg+ 01 P3+ 03 Then sin maybe found by dividing the values of (ka sin 5) in the first column ofTable II by ka.

It is worth noting that a given disk may be made to resonate in aspecified normal mode, say with nodal circles, by determining thefrequency from (32). Then (46) gives the value of k and the column(Pn+Qn) in Table II gives the values of pressure to be plotted vs. thevalues of obtained as explained above. Thicker disks may be made toresonate in the same normal mode by increasing the frequency. The valuesof pressure are found in the same column as before but, since It isincreased, the values of corresponding to a given set of values of(Pn+Qn) are decreased. The result is a folding of the side lobes towardthe axis.

The graphs of (Pn-I-Qn) vs. (ka sin 5), shown in Figure 4 of the drawingfor 1L.=1, 2, and 3 respectively, show that the functions pass throughSuccessive maximum and minimum values or peaks as (lca sin increases. Ifit is des'red to design a disk so that, when vibrating at resonance in abafiie, it will have a given number of nodal circles and will have adirectional characteristic relative to the disk with a side lobe whosemaximum value is at some specified angle from the axis of the disk, itis only necessary to select a maximum or minimum point on the curve(Pn+Qn), where n is taken as the number of nodal circles, and determinethe corresponding value of (lea sin c). With known the value of k may befound as the value of (Ice sin divided by (a sin Then, from (45.)

and, from (32) If the maximum or minimum point selected is the firstsuch point on the curve, the corresponding side lobe will be the firstlobe from the axis. If it is the second such point, the lobe will be thesecond from the axis and so on. If the first maximum or minimum point onthe curve of (Pn+Qn) is very small relative to the second such point thefirst side lobe maybe negligible relative to the second side lobe. .Insuch a case the disk may be designed to vibrate at a relatively lowfrequency with the first side lobe in the desired position or at ahigher frequency with the second side lobe in the desired position. The

i2 directional patterns would not be identical but would be similar. Itis noted'that the principal maximum or minimum corresponds to the numberof nodal circles involved, i. e., for P3+Q3, corresponding to threenodal circles, the principal deviation is the third loop.

To illustrate the procedure used to choose a suitable disk or diaphragmI9, assume that it is desired to design a disk 2.54 cm. in diameterwhich would vibrate with one nodal circle and radiate most of the soundat an arbitrary angle from the axis. Choosing 67, for such an angle, thefrequency of operation for such a disk, i. e., the driving frequencyused to drive or excite the disk, is obtained from the graph of (P1+Q1)in Fig. 4 by first finding the value of (ka sin qb) corresponding to thefirst minimum, namely 3.8. Substituting the values of and a in (ka sin)=3.8 gives k==3.25 or i=17.8 10 ,C. P. S. Substituting this value for,f as well as the values of E, 11 and A, in (32) h=0.19 cm. Since thisparticular value of h does not correspond to a standard gauge of brass,assume use of the nearest standard gauge (0.211 cm.). The calculatedresonant frequency for the 0.211 cm. disk is then 19.7 kc. and thecorresponding angle of maximum radiation is 56.

The calculated pressure distribution at resonance for the 0.211 cm. diskmounted in an infinite bafile is shown in Fig. 9. The actually measureddistribution pattern for the frequency which gave the minimum pressureon or near the axis is shown in Fig. 10. The actual frequency used forthe measured curve is 19.2 kc. instead of 19.7 kc. When this disk ismounted in the parabolic horn, the beam obtained is sharp and theamplitude of the largest side lobe is only 0.12 times the amplitude ofthe main beam. The sand pattern for this disk is shown in Fig. 11.

Inasmuch as the diaphragm I9 is associated with the reflector 20, it isseen that the sharpness of the radiated beam is determined by therelative amount of radiation directed towards the side walls of the hornor reflector 2|] when the vibrating disk is chosen in accordance withthe above analysis. When used as a blind-aid device, sharpness of theradiated beam aids in distinguishing between objects'which are closetogether and hence for such a purposeit is particularly desirable that apredominant part of the radiation be toward the side walls of. thereflector 20.

:In other words. wide angle radiation with respect although there shouldbe suflicient clearance between the diaphragm and the reflector to,prevent interference with free movementof thediaphragm. The end of thereflector thus substantially closed off by the diaphragm I9 mayberemoved as shown. in Fig. 2, leaving an opening of substantially thesame area as the diaphragm I9.

- The reflector preferably has an opening 23 opposite the opening 2I .ofdiameter large relative "to the wave length of the frequency of theradiations in air. In order to determine the proper :size of the opening23, Equation .42 may be used inwhic'h the radius of the opening 23 ofthe 13 =reflector 20 is substituted for the radius of the diaphragm I9.I

In order to obtain maximum sensitivity, the ctube [4 should have alength of approximately one-fourth'wave length with respect to the wavelength of the compressional waves in the tube M. It may be noted thatthe frequency of vibration is the same throughout the system but thewave length differs according to the medium through which the waves arepassing. The tube l4 may be slit lengthwise in order to reduce eddycurrents. It has been found that the diameter of the tube I4 isrelatively immaterial except that if the diameter of the tube is thesame as the diameter of a nodal circle, it is difficult to excite thedial phragm inthe desired mode. It has been found that best results areobtained if the tube is .joined to the diaphragm at a point where thediaphragm, remains substantially perpendicular to the adjacent tubesurface at all degrees of Vibra- 'tion, 1. e., the slope of the surfaceof the diaj'phragm ,at the medium is substantially zero, not only in theabsence of driving force, but also during vibration at the-desiredfrequency. This condition is met if the diameter of the tube is equal tothe diameter of a median between two normal circular modes. While such alocation is preferred, it has been found that if the connection betweenthe tube is and the diaphragm I9 is such that the shape of the dynamiccurvev "of the disk, i. e., the cross-sectional contour of :the diskwhen vibrating, is not aifected, the tube diameter is relativelyimmaterial with the one exception already noted that the tube should nothave the same diameter as a nodal circle. It has been found that asoldered joint provides such aconnection. Thus, if a-connection is madeat a median between nodal circles, no difficulty is experienced. If thetube is connected otherwise except close to a nodal circle, satisfactoryopera- .tion results if the disk or diaphragm I9 is rela- ,tively thick.From the foregoing, it would ap- ;pear to follow that with only onenodal circle, the connection between the tube I4 and diaphragm is shouldbe made at the exact center of the diaphragm. Since it is difficult toget good mechanical support from a small tube or rod, a tube ofsubstantial dimensions must be used forpractical reasons so that with aone nodal circle mode,.a

relatively thick diaphragm i9 is preferably used.

preferably fiat. This condition does not prevent.

connection of the tube is at the outer edge of the diaphragm IS. Thenecessary condition can 'be met if a sufiiciently thick diaphragm isemployed, and the connection or joint between diafphragm and tube issufficiently flexible to permit the necesary movement of the diaphragmedge relative to the tube i4. Itv has been discovered that all circularmodes "are not satisfactory but only normal. circular modes give thedesired results; the diametenof each nodal circle must bear a certainrelation to the diameter if the diaphragm l9 and the necessary relationis met if the diaphragm l9 satisfies Equations 32, 41, 42, and 43. Fig.7 gives an indication of the appearance of side lobes (undesirable inmost directional beam devices) resulting from a non-normal single circlemode. of which Fig. 8 is-a sand pattern.

For results obtained from acne nodal circle eperation, see Fig. 11, thedirectional pattern be- In other words,

'ing similar to Fig. 5. Fig. 5, there is represented a typicaldirectional beam obtained from a transducer utilizing a two nodal circledrive, a sand pattern of the two nodal circles being shown in F g. 6.

While a parabolic reflector has been described and illustrated inconnection with theforegoing description, any reflecting means may beemployed which will direct the radiation from the diaphragm l9sufficiently parallel to and symmetrical with respect to the axis of thediaphragm to establish a radiated beam of satisfactory configuration.

Other modifications will occur to those skilled in the art. For example,referring to Equation 10, if :01; be a. constant equal to 3.01, 6.21,9.37, etc. depending on the number of nodal circles and f is substitutedfor A, Equations 9 and 10 may be combined to give the formula If v betaken as /3, at" will equal 3.01, 6.21, 9.37, etc. Formula 32 then maybe written Approximate satisfaction of the equation providessatisfactory results in most, if not all, cases, because of variationsin material.

Similarly Equation 320. may be written where 2n is a constant dependingupon the number of nodal circles desired. Expressions 49 and 51 disclosethe relationship between frequency, thickness of diaphragm and radius ofdiaphragm.

What we claim is:

I 1. In a transducer of the type having a parabolic reflector, adisk-like diaphragm arranged for vibration as a free-edge disk andlocated substantially at the plane of the latus rectum of saidreflector, a member of magnetostrictive character connected to saiddiaphragm, means including said member for causing said diaphragmtovibrate, said member being connected to said'diaphragm at that locationof said diaphragm at which the slope remains substantially zero duringvibration at said desired frequency.

2. In a transducer of the type having a para bolic reflector, adisk-like diaphragm arranged for vibration as a free-edge disk andlocated substantially at the plane of the latus rectum of saiddiaphragm, a tube of magnetostrictive character secured against motionat one portion thereof relative to said reflector and connected to saiddiaphragm at another portion thereof, means including said tube forcausing said diaphragm to vibrate, said member being connected to saiddiaphragm at a location thereof which has minimum displacement duringvibration at said desired frequency, the distance between said portionsof said tube beingof the order of one quarter wavelength in length withrespect to the wavelength of the compressional wave in said tube.

3. In a transducer having a parabolic reflector, a diaphragm arrangedfor vibration as afrees,

i edge disk and. disposed normal to the axis or said reflector atsubstantially the plane of the: latus rectum. thereof, a cylindrical;tube of magnetostrictive character connected to said diaphragm, meansincluding said tube for causing said diaphragni to vibrate in accordancewith signals to beemitted from said reflector, said. diaphragm beingdimensioned such that said diaphragm "vibrates in a normal circular modeof at least two nodal circles, the diameter of said tube being such thatsaid tube is connected to said diaphragm at substantially the medianbetween two of said nodal circles.

4,111 a transducer comprising parabolic reflector, the diaphragmarranged for vibration as a free-edge disk at substantially the plane ofthe latus rectum of said reflector, and means for driving said diaphragmat a desired frequency, the approximate dimensions of said diaphragmbeing chosen according to the formula W h: E :03,

21r 12p(1v a? in which f is the frequency of vibration, h is thediaphragm thickness in cm., a is the radius of the diaphragm, E isYoungs modulus of elasticity of the diaphragm material, p is the densityof the diaphragm material, 1/ is Poisson's ratio for the diaphragmmaterial and $12 is a constant dependin upon the number of nodal circlesdesired and determined as the roots of the equation x rt' -l Mr) inwhich J0, J1, I, and I1, are the usual notations for Bessel functions.

5. In a transducer comprising a parabolic refiector, a diaphragmarranged for vibration as a free-edge disk and located substantially atthe plane of the latus rectum of said reflector, and means for drivingsaid diaphragm at a desired frequency, the approximate dimensions ofsaid diaphragm being chosen according to the formula h f Z1185 in whichis the frequency of vibration, h is the thickness of the diaphragm, a isthe radius of the diaphragm, and Zn is a constant determined by thematerial from which the diaphragm is made and the desired normal mode ofvibration of said diaphragm.

6. In a transducer comprising reflecting means, a diaphragm arranged forvibration as a freeedge disk, and means for exciting said diaphragm at adesired frequency, the approximate dimensions of said diaphragm beingchosen to satisfy the equation ratio for the diaphragm material, a isthe radius of" the diaphragm, and an is a constant depending upon thenumber of nodal circles desired and determined as the roots of theequation ai -12mm w 1( 1( in which Jb, Ji, It, and I1, are the usualnotations for Bessel functions.

7; Iii a transducer comprising a parabolic re fiector, a diaphragmarranged for vibration as a free edge disk at substantially the plane otthe latus" rectum of said reflector, and means for driving saiddiaphragm at a desired frequency. the ap roximate dimensions of. said.diaphragm being chosen: to satisfy the formula I where h is thethickness of the diaphragm, a is the radius of the diaphragm, j is thefrequency of vibration. and is approximately equal to M10 /l,.8-25 (Jcbeing determined from the value of Ira, sin it in which 4 represents theangle of radiation corresponding to a peakof. the dynamic curve of saiddiaphragm other thanv the principal peak) E is Youngs modulus ofelasticity of'tlie diaphragm material,- p is the density of thediaphragm material, 1! is Poissons ratio for the diaphragm material. andx is a constant depending upon the number of nodal circles desired andis determined as the roots of the equation nrp hw Mo :0 J1(x)' I .(x)"

which J 0,. J 1, Io, and Ii,- are the usual notations for: Besselfunctions.

8. An article of. manufacture comprising a circular diaphragm having.dimensions conforming to" the formula T d 10%) a: J Am) l tzt) in which.J0, J1, I0 and I1, are the l'iSllalnotations for Bessel functions.

9. An article of manufacture comprising a circular diaphragm havingdimensions conforming to the formula in which ,f, is the frequency ofvibration, it isft he thickness of thediaphragm, a is the radius of thediaphragm, and a is a constant determined by the materiai from which thediaphragm made and the desired normal mode oi vibrationof saiddiaphragm.

10. Anarticle of manufacture comprising a circular diaphragm havingdimensions conforming to the. equation in which j is the frequency ofvibration, it is the diaphragm thickness in cm., E is Young's modulus ofelasticity of the diaphragm material, p is the density of the diaphragmmaterial, 11 is Poissoii s' ratio for the diaphragm material, a is theradius of the diaphragm and is a constant depending- 1 7 upon the numberof nodal circles desired and determined as the roots of the equation a:J 1 M in which J0, J1, for Bessel functions.

11. An article of manufacture comprising a circular diaphragm havingdimensions conforming to the formula diaphragm material, p is thedensity of the diaphragm material, 11 is Poissons ratio forithediaphragm material and $11 is a constant depending I0, and I1, are theusual notations 5 18 upon the number of nodal circles desired and isdetermined as the roots of the equation Jo( o( 1v 1( 1( in which J0, J1,I0 and I1 are the usual notations for Bessel functions.

FRANK H. SLAYMAKER.

WILLARD F. MEEICER. LYNN L. MERRILL.

REFERENCES CITED The following references are of record in the file ofthis patent:

UNITED STATES PATENTS Number Name Date 1,399,877 Pupin Dec. 13, 19211,676,625 Walker July 10, 1928 2,063,944 Pierce Dec. 15, 1936 2,074,266'Koch Mar. 16, 1937 2,135,840 Pfister Nov. 8, 1938 2,216,380 VoightlanderOct. 1, 1940 2,403,990 Mason July 16, 1946 orrection Patent No.2,541,944

FRANK H. SLAYMAK R ET AL.

fication of pears in the printed spec It is hereby certified that errorap the above numbered patent requiring correction as follows: line 62,for Moa read M /a; column Column 7, (Pn-l-Qn) read (P'n-l- Qn) and thatthe said Letters Patent should be read as corrected above, so that thesame may conform to the record of the case in the Patent Oflice.

Signed and sealed this 11th day of September, A. D. 1951.

9, line 61, for

THOMAS F. MURPHY,

Assistant Commissioner of Patents.

Certificate of Correction Patent No. 2,541,944: February 13, 1951 FRANKH. SLAYMAKER ET AL.

It is hereby certified that error appears in the printed specificationof the above numbered patent requiring correction as follows:

Column 7, line 62, for Moa read lil /a column 9, line 61, for (Pn+2n)read (Pn+ Qn) and that the said Letters Patent should be read ascorrected above, so that the same may conform to the record of the casein the Patent Oflioe. Signed and sealed this 11th day of September, A.D. 1951.

THOMAS F. MURPHY,

Assistant Oommz'ssz'oner of Patents.

